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On each turn you roll the dice twice. If you roll the same number twice then...

On each turn you roll the dice twice. If you roll the same number twice then you win and if you don't then you lose. You start with 100 tokens and if you win then you get 5 tokens and if you lose you lose 2 tokens. After 36 turns, how many tokens will you have?

Math   Statistics-And-Probability   
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Answer #1

P(winning) = P( you got same number on two roll ) = P( {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6) } ) = 6/36 = 1/6

P(losing) = 1 - P(winning) = 5/6

After 36 turns expectation of winning = 36 * P(winning) = 36 * 1/6 = 6

Tokens gained by 6 wins = 5 * 6 = 30

After 36 turns expectation of losing = 36 * P(losing) = 36 * 5/6 = 30

Tokens lost by 30 loses = 2 * 30 = 60

Expected remaining tokens after 36 turns = 100 + tokens gained by 6 wins - tokens lost by 30 loses = 100 + 30 - 60 =70

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